Looks like its just your PHP formatting, you have the right idea! try this:
<pre class="prettyprint"><code class="language-php">
<?php
if (is_page( 'Home' ) {
$class="active";
}
elseif (is_page( 'About' ) {
$class="active";
}
else {
$class="";
}
?>
<li class="<?php echo $class; ?>"Home</li>
<li class="<?php echo $class; ?>"About</li>
</code></pre>